Constraint nonlinear model predictive control for trajectory tracking of a quadrotor using linear matrix inequalities

This paper introduces a robust nonlinear model predictive control (NMPC) framework for quadrotor unmanned aerial vehicles (UAVs), addressing their nonlinear, underactuated dynamics and operational constraints. The continuous-time infinite-horizon NMPC problem is reformulated via convex linear matrix inequality (LMI) conditions to ensure feasibility and closed-loop stability. In contrast to conventional first-order LMI approximations, a second-order Taylor approximation is employed, enhancing model fidelity and control performance. Uncertainties, external disturbances, and actuator saturation are explicitly incorporated, guaranteeing robust stability under bounded disturbances. Simulation results demonstrate superior performance of the proposed MPC-LMI controller over the Linear Quadratic Regulator (LQR) and conventional MPC, with average reductions of 66 % in Integral Square Error (ISE) and 33 % in Mean Absolute Value (MAV) relative to LQR, and 79 % in ISE and 37 % in MAV relative to conventional MPC. The approach is computationally efficient and scalable, extending its applicability to a broad class of nonlinear systems.